Ice surfaces: macroscopic effects of microscopic structure By J. S. Wettlaufer Applied Physics Laboratory and Department of Physics, Box 355640, University of Washington, Seattle, WA 98105, USA ([email protected]) The balance between ice and water controls the habitability of an important fraction of the globe and influences the majority of the world’s population. The freezing of water to form ice is one of the most common phase transformations in the natural environment. However,a complete understanding of its microscopics and their influ- ence on macroscopic phenomena still eludes us. As this millennium comes to a close, we are beginning to understand how the microscopic interfacial structure of ice con- trols pattern formation during ice-crystal growth,the evolution of the polycrystalline fabrics of the great ice sheets,the dynamics of ground freezing,ozone destruction, and the mechanism of charge transfer that drives thunderstorm electrification. This paper describes our evolving understanding,its implications for the basic principles of melting and freezing,and their environmental consequences. Keywords: premelting; ice; phase transitions; surfaces; disorder; environment 1. Introduction More than two-thirds of our planet’s surface is covered by water. Our mean distance from the Sun,the geometry of our orbit,and the radiative properties of our atmo- sphere contrive to make the mean surface temperature ca.15◦C; 25 ◦C in the large tropical and subtropical belt,and between −20 and −40 ◦C in the small polar caps. Water becomes ice at just around the middle of that temperature range. Only a small shift in temperature determines whether precipitation will fall as rain or as snow and whether an ocean region will be blue water or white ice. It is no wonder,then,that ice cover is an extremely sensitive geophysical variable,and that ice has innumerable and profound consequences for climate,the hydrological cycle,vegetation and all other elements of the biosphere,land forms,and,hence,all human activities. Many aspects of its microphysics and chemistry have large-scale consequences. The difficulties associated with observing processes in their natural setting often impede our ability to extract the essential features,and,hence,controlled labora- tory experiments play a significant role in the development of our understanding. Our exploration of these phenomena,and the challenges that they offer,begins at a microscopic scale,on the surface of ice,and moves toward larger scales. The chal- lenges encountered are at least as old as science itself. Phil. Trans. R. Soc. Lond. A (1999) 357, 3403–3425 c 1999 The Royal Society 3403 3404 J. S. Wettlaufer 2. History One may argue that the strikingly detailed observations of snow and ice made during the winter of 1635 by Descartes initiated the scientific method. Among other things, his work highlighted the role of ice surfaces in its melting and adhesive behaviour (Frank 1974). Over 200 years later,in 1842,Michael Faraday began a 20 year inves- tigation into the properties of snow and ice. Faraday’s publications based on this research (see,for example,Faraday 1860) clearly demonstrate the notion that melt- ing and freezing are influenced by the interfaces that separate solids from liquids. Two pieces of thawing ice,if put together,adhere and become one; at a place where liquefaction was proceeding,congelation suddenly occurs ...a particle of water,which could retain the liquid state while touching ice only on one side,could not retain the liquid state if it were touched by ice on both sides; but became solid,the general temperature remaining the same. Although Faraday and Tyndall’s (Tyndall 1858) experiments were proof to them that an interfacial film of liquid existed at equilibrium,their powerful contempo- raries,James Thomson and his brother Sir William Thomson (who later became Lord Kelvin),countered with an explanation growing out of their work on the influ- ence of pressure on phase changes,arguing that regelation,which is now called sin- tering,of ice results from the temporary lowering of the melting temperature due to the increase of pressure at the points of contact. Faraday argued that the pressure- melting experiments did not have sufficient resolution to resolve the dispute,and that ...experiment might be so applied as to advance the investigation of this beautiful point in molecular philosophy to a further degree than has yet been done; even to the extent of exhausting the power of some of the principles assumed in one or more of the three views adopted,and so render our knowledge a little more defined and exact than it is at present. Despite Faraday’s call for refined study,pressure melting came to be the textbook explanation for the rapid sintering and slipperiness of ice. However,simple calcula- tion shows that pressure melting cannot account for the low friction of ice except at temperatures very close to the normal melting point; for a typical person on a conventional ice skate,the depression of the melting point is less than 0.1 K. At lower temperatures,as was argued by Bowden & Hughes (1939) and as developed further by Evans et al. (1976),the low-friction coefficient in ice skating is due to frictional heating. Nonetheless,for an explanation of Faraday’s observations we require a more general phenomenon,found in virtually all forms of solid matter. 3. The surface of ice Imagine moving toward the surface of an ice crystal from deep within its interior. During your transit along a crystallographic axis you encounter molecules with peri- odic regularity,each molecule being coordinated with its nearest neighbours. How- ever,the coordination becomes distorted as you near the crystal’s surface where the Phil. Trans. R. Soc. Lond. A (1999) Ice surfaces: macroscopic effects of microscopic structure 3405 (a)(b) Figure 1. A simulated molecular scale picture of the surface region (the top of the picture) at the primary crystallographic orientations of ice: (a) the basal facet and (b) the prism facet. The liquid-like disordered structure appears at the surface at temperatures below the bulk melting temperature, and its extent depends on the underlying crystallographic structure and the temperature. The large solid circles are the oxygen atoms and the small dots are the hydrogen atoms averaged over 10 ps at a temperature 8 K below the bulk melting temperature (from the molecular dynamics simulations of Furukawa & Nada (1997)). The upper (lower) arrows indicate the ‘quasi-liquid’ layer (bulk ice crystal). More accurate intermolecular potentials are being developed (Batista 1999) that will improve such simulations. molecules are the most poorly bound and,relative to those in the interior,experience the greatest deviation from the crystal’s harmonic structure. At higher temperatures,thermally activated fluctuations cause the greatest vibra- tions at the surface and,at a sufficiently high temperature but still below the melting point,intermolecular bonds rupture and eventually molecules begin to flow in a film confined to the surface; a kind of quasi-liquid,with some structural characteristics of the solid below,but with the mobility of a fluid (figure 1). When one first hears the term ‘surface melting’ one’s natural reaction is to imagine how a solid,as it is heated,melts from its surface inward. This kind of example,first considered by Tammann (1909),is analogous to a lump of solder under a soldering iron,which begins to liquefy at its surface simply because the outside is hotter than the inside; the melting process is limited by the transient flow of heat. Our modern description of surface melting specifically refers to a less obvious effect: the surface of a solid,at a uniform temperature,develops a thin coating of its melt at temperatures below the bulk transition temperature. The layer is a stable and reversible characteristic of the equilibrium state. It is a precursor of the complete melting of the solid,and it is a very general property of nearly all solid matter, influencing crystal growth,adhesion and other behaviour (Wettlaufer 1999 a). Metals, semiconductors,solid rare gases and molecular solids,including ice,undergo the Phil. Trans. R. Soc. Lond. A (1999) 3406 J. S. Wettlaufer (a) vapour liquid d d d solid T T T1 2 3 (b) 25 15 200 20 10 15 5 100 10 0 10.0 1.0 0.1 film thickness (Å) no. of molten layers 5 Tm – T (K) T surface peak area (monolayer) m 0 300400 500 600 –1.0 –0.5 0 temperature (K) temperature (°C) Figure 2. (a) Surface melting is a general phenomenon. It is a special case of wetting, wherein the ‘substrate’ is the solid phase of the liquid melt. If the cohesive forces in a fluid are stronger than the adhesive forces of attraction between the substrate and the fluid, the latter stands as a droplet with a finite contact angle, rather like water droplets on a freshly waxed car. If the intrafluid forces are weaker than the adhesive forces, the droplet spreads to completely wet the surface. Such is the case for surface melting. As the temperature rises, T1 <T2 <T3, the film thickness increases as depicted here, and illustrated in (b) for two different materials. (b) The figure on the left shows the thickness of the surface-melted layer on the (110) face of a lead crystal, measured by Frenken & van der Veen (1985) using the technique of ion backscattering. The right-hand vertical axis is the number of monomolecular layers and the bulk melting temperature is denoted by Tm. On the right, we see the thickness of the surface-melted layer on the basal plane of ice, obtained by Elbaum et al. (1993) using the technique of optical reflectometry.